Question

Triangle XYZ is isosceles. The measure of the vertex angle, Y, is twice the measure of a base angle.

What is true about triangle XYZ? Check all that apply.

Answer 1

a. Angle Y is a right angle.

b. The measure of angle Z is 45°.

e. The perpendicular bisector of creates two smaller isosceles triangles.

Explanation:

Let x represent the measures of base angles X and Z. Then 2x is the measure of vertex angle Y, and the sum of angles is ...

x + x + 2x = 180°

x = 45°

2x = m∠Y = 90°

so the triangle is an isosceles right triangle which has base angles of 45°.

The perpendicular bisector of XZ is the altitude of the triangle XYZ. It creates two smaller right triangles with acute angles of 45°. Hence, those, too, are isosceles right triangles.

Answer 2

let the vertex angle = 2x degrees then the 2 base angles will both be x
So we have
2x + x + x = 180
4x = 180
x = 45

So the triangle will be right angled and have angles 45-45-90 degrees.